复Finsler流形上的Koppelman-Leray-Norguet公式

利用不变积分核(Berndtsson核),复Finsler度量和联系于Chern-Finsler联络的非线性联络,研究复Finsler流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的积分表示,得到了(p,q)型微分形式的Koppelman-Leray-Norguet公式和■-方程的解．作为应用,利用复Finsler度量和联系于Chern-Finsler联络的非线性联络,给出了Stein流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的Koppelman- Leray-Norguet公式以及■-方程的解,并且得到了Stein流形上实非退化强拟凸多面体上(p,q)型微分形式的积分表示式和■-方程的解．

The Koppelman-Leray-Norguet Formulas on Complex Finsler MAnifolds

By means of the invariant integral kernel (the Berndtsson kernel),com- plex Finsler metric and non-linear connection associated with Chern-Finsler connec- tion to research the integral representations for the differential forms of type (p,q) on a bounded domain with piecewise smooth C~((1)) boundaries on a complex Finsler manifold, the Koppelman-Leray-Norguet formulas are obtained,and the ■-equations are solved. As an application,with the help of the complex Finsler metric and non-linear connec- tion associated with Chern-Finsler connection,we give the Koppelman-Leray-Norguet formulas of (p,q) differential forms and the solutions of ■-equation on a bounded do- main with piecewise smooth C~((1)) boundaries on a Stein manifold.Moreover,we obtain the integral formulas of (p,q) differential forms and the solutions of ■-equation on a real non-degenerate strictly pseudoconvex polyhedra on a Stein manifold.